I am a professional portrait photographer. I currently run the portrait studio my father started in 1971. We converted to digital in 1997 and our first digital camera was $28,000. The last camera I bought was $1400 and produces images far superior to anything we ever captured on medium format or 35mm film.
As with any tool, a camera can produce great results or really crappy results. Proper composition, focus, exposure, and many other elements make a great image. If any of those elements are out of whack, then the image suffers.
Film is more forgiving of improper exposure. In digital, an overexposed image may not have any detail in the highlights, whereas film will still have those details. A professional photographer who captures RAW files and properly exposes the image can make far more adjustments in Photoshop to produce a perfect image with great contrast and saturation. Being able to see the image on an LCD at the time of capture along with Histogram information makes dialing in the exposure even easier. This is especially important when balancing multiple light sources.
Digital has given me a tool that allows me to have more control over my final images than film allowed. I currently have digital images I have created on 7 different billboards, so digital images enlarge just fine as well.
Also, I have my own lab and print our images in house on true photographic paper (i.e. Silver Halide) which uses color devloper, bleach fix, and stabilizer. The printer uses an Micro Light Valve Array with fiber optics to transfer the digital data to analog exposure on the paper. These prints will last as long as any traditionally printed film portrait since the actual printing is the exact same. However, as inkjet and other dry processes mature in the coming years, I suspect "wet photo processing" will be a thing of the past.
Now, none of this is really of much importance to non-professionals, so let me say this: A $100 point-and-shoot digital camera will usually produce much better results than a similarly priced point-and-shoot 35mm film camera. Just pop out the SD card and take it to Wal-Mart and have them make you 4x6 prints. They'll look great.